Spectral Functions in Mathematics and Physics / Edition 1

by Klaus Kirsten

Overview

The literature on the spectral analysis of second order elliptic differential operators contains a great deal of information on the spectral functions for explicitly known spectra. The same is not true, however, for situations where the spectra are not explicitly known. Over the last several years, the author and his colleagues have developed new, innovative methods for the exact analysis of a variety of spectral functions occurring in spectral geometry and under external conditions in statistical mechanics and quantum field theory.

Spectral Functions in Mathematics and Physics presents a detailed overview of these advances. The author develops and applies methods for analyzing determinants arising when the external conditions originate from the Casimir effect, dielectric media, scalar backgrounds, and magnetic backgrounds. The zeta function underlies all of these techniques, and the book begins by deriving its basic properties and relations to the spectral functions. The author then uses those relations to develop and apply methods for calculating heat kernel coefficients, functional determinants, and Casimir energies. He also explores applications in the non-relativistic context, in particular applying the techniques to the Bose-Einstein condensation of an ideal Bose gas.

Self-contained and clearly written, Spectral Functions in Mathematics and Physics offers a unique opportunity to acquire valuable new techniques, use them in a variety of applications, and be inspired to make further advances.

Product Details

ISBN-13:	9781584882596
Publisher:	Taylor & Francis
Publication date:	12/13/2001
Pages:	396
Product dimensions:	6.12(w) x 9.19(h) x (d)

About the Author

Klaus Kirsten is a post-doctoral associate at the Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany.

Table of Contents

Introduction. A First Look at Zeta Functions and Heat Traces. Zeta Functions on Generalized Cones and Related Manifolds. Calculation of Heat Kernel Coeffcients via Special Cases. Heat Content Asymptotics. Functional Determinants. Casimir Energies. Ground State Energies under the Influence of External Fields. Bose-Einstein Condensation of Ideal Bose Gases under External Conditions. Conclusions. Appendices. References. Index.

Editorial Reviews

Presents new methods for the exact analysis of spectral functions under external conditions, focusing on zeta functions of second-order elliptic differential operators. The first technique analyzes spectral functions for Laplace-type operators for cases where the spectrum is not known explicitly, but only implicitly. The author applies the methods to derive heat kernel coefficients for smooth Riemannian manifolds with various boundary conditions, functional determinants, Casimir energies with spherically symmetric boundaries, and the Bose-Einstein condensation. Annotation c. Book News, Inc., Portland, OR (booknews.com)